Download Lesson 1.1.3

Introduction
Mathematical expressions are commonly used to
represent real-world scenarios that involve a changing
variable. For example, an expression can be written to
show the total number of miles run in a week, the total
cost of clothes bought at a sale, the profit of a business,
and how to evenly divide cookies amongst friends. There
are many key parts of an expression, including terms,
constants, and coefficients.
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1.1 Skill 3: Identifying Parts of an Expression
Key Concepts
• An expression is a combination of variables,
quantities, and mathematical operations. Some
examples of expressions are 4, 8x, and b + 102.
• Expressions are made up of terms, which can consist
of a number, a variable, or the product of a number
and variable(s).
• To find the number of terms in an expression,
determine how many parts of the expression are
separated by an operation (+, , , or ). For example,
the expression 3x + 4y has two terms, 3x and 4y.
The expression 5z2  8x + 7 has three terms: 5z2, 8x,
and 7. The expression 12 has one term, 12.
1.1 Skill 3: Identifying Parts of an Expression
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Key Concepts, continued
• Remember that a variable is a letter used to
represent a value or unknown quantity that can
change or vary. The variables in the expression
6x3 + 2y  3 are x and y.
• A coefficient is the number multiplied by a variable in
an algebraic expression. The coefficients for the
expression 3x + 4y are 3 and 4, the coefficients for the
expression 5z2  8x + 7 are 5 and 8, and the
coefficient for the expression x + 7 is 1.
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1.1 Skill 3: Identifying Parts of an Expression
Key Concepts, continued
• A constant is a quantity that does not change. The
constant term for the expression 5z2  8x + 7 is 7.
Given the expression 12, 12 is already a constant
term.
• The four main mathematical operations are addition,
subtraction, multiplication, and division.
• The result of adding is called a sum. An example of an
expression which contains a sum is 4x + 8z.
• The result of subtracting is called a difference.
An example of an expression that contains a difference
is 4x  8z.
1.1 Skill 3: Identifying Parts of an Expression
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Key Concepts, continued
• The result of multiplying is called a product. An
example of an expression that contains a product is
4x • 8z.
• The result of dividing is called a quotient. An example
4x
of an expression that contains a quotient is
. It is
8z
the result of dividing 4x by 8z.
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1.1 Skill 3: Identifying Parts of an Expression
Guided Practice
Example 3
Nia bought 4 packs of pencils (p) and 6 packs of index
cards (c) at the school store, which does not charge any
tax. She had a coupon for $2 off her total purchase.
Write an expression to represent Nia’s purchase, and
then identify the terms, coefficients, and constant term
(if applicable) in the expression.
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1.1 Skill 3: Identifying Parts of an Expression
Guided Practice: Example 3, continued
1. Write an expression to represent Nia’s
purchase.
In order to write the expression for Nia’s purchase,
first identify each term of the expression.
Pencils are represented by the variable p, and Nia
bought 4 packs of pencils. The term representing the
number of pencils she purchased is 4p.
Index cards are represented by the variable c, and
she bought 6 packs of index cards. The term
representing the number of packs she purchased
is 6c.
1.1 Skill 3: Identifying Parts of an Expression
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Guided Practice: Example 3, continued
Nia had a coupon for $2 off her total purchase.
The coupon represents a discount, or subtraction,
from the amount she has to pay. This can be
represented by –2.
Combining the terms, the expression that represents
Nia’s purchase is 4p + 6c – 2.
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1.1 Skill 3: Identifying Parts of an Expression
Guided Practice: Example 3, continued
2. Identify the term(s) in the expression.
The expression representing Nia’s purchase is
4p + 6c – 2. Terms can be a number, a variable, or
the product of a number and variable(s). The terms
are 4p, 6c, and –2.
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1.1 Skill 3: Identifying Parts of an Expression
Guided Practice: Example 3, continued
3. Identify the coefficient(s) in the
expression.
A coefficient is a number multiplied by a variable in an
algebraic expression. In the expression 4p + 6c  2,
the coefficients are 4 and 6.
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1.1 Skill 3: Identifying Parts of an Expression
Guided Practice: Example 3, continued
4. Identify the constant term(s) in the
expression, if any.
A constant is a quantity that does not change. In the
expression 4p + 6c  2, the constant is 2.
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1.1 Skill 3: Identifying Parts of an Expression
Guided Practice: Example 3, continued
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1.1 Skill 3: Identifying Parts of an Expression